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W 1. Suppose we require “proof beyond reasonable doubt” to be a “significance level of 5%. This means, P{conclude better | not effective} is 5% (or less). In many applications we cannot accurately estimate P{conclude better effective} unless we actually know how much better the treatment really is. Let us suppose that P{conclude better effective} is 60%. Imagine that there are thousands of researchers doing these experiments, each testing some hypothesis they have proposed. Let us assume that only in 4% of cases is the treatment really effective (it is not easy to find good treatments). 1 of 2 GSC 1206 Introduction to Data Analytics for Business Fall 2021 a. Construct a tree diagram that will show all possible outcomes of effective (not effective) and conclusions (better or not better). Label each branch with respect to the event associated with the branch and the probability of travelling along the branch. Total b. Summarize the outcomes in a probability table such as Treatment not Treatment effective effective Conclude treatment not better Conclude treatment better Total 100% C. What is the probability that you will conclude that the treatment is effective? d. Among cases where you conclude the treatment is effective, what proportion really are effective?